The plague doctors known to all wore a special mask with a beak. However, this beak was not intended to intimidate: they wore a variety of strong-smelling substances, such as cloth soaked in vinegar, flowers, herbs, or camphor.
It was believed that the plague spread through special "miasmas," and such a peculiar filter was supposed to stop them. By the way, this costume appeared only in the XVII century, so it has nothing to do with the Middle Ages.